Answer:
(a) ω= 7 rad/s
(b) θ= 22.5 rad
(c) at = 10 cm/s²
Step-by-step explanation:
The uniformly accelerated circular movement, also called uniformly varied circular movement is a circular path movement in which the angular acceleration is constant.
There is tangential acceleration (at ) and is constant.
at = α*R, where R is the radius of the movement
We apply the equations of circular motion uniformly accelerated :
ω= ω₀ + α*t Formula (1)
θ= ω₀*t + (1/2)*α*t² Formula (2)
at = α*R Formula (3)
Where:
θ : angle that the body has rotated in a given time interval (rad)
α : angular acceleration (rad/s²)
t : time interval (s)
ω₀ : initial angular speed ( rad/s)
ω : final angular speed ( rad/s)
R : radius of the circular path (cm)
at: tangential acceleration, (cm/s²)
Data:
R= 10 cm : radius of the disk
t₀=0 , ω₀ = 2 rad/s
α= 1 rad/s2
t = 5 s
(a) Disk’s angular velocity at t = 5.0 s
We replace data in the formula (1)
ω= ω₀ + α*t
ω= 2 + ( 1 )*(5)
ω= 7 rad/s
(b) Angle that the disk has rotated in t = 5.0 s
We replace data in the formula (2)
θ= ω₀*t + (1/2)*α*t²
θ= (2)*(5)+ (1/2)*(1)*(5)²
θ= 10+ 12.5
θ= 22.5 rad
c) Tangential acceleration of a point on the disk at t = 5.0 s
We replace data in the formula (2)
at = α*R
at = (1)*(10)
at = 10 cm/s²